Question

Find the gradient of the line l1 which has equation 4x-3y+5=0 .

Answer 1

To find the gradient of the line with the equation 4x-3y+5=0, rearrange it to the slope-intercept form to yield y=(4/3)x+(5/3), where the gradient is 4/3.

Step-by-step explanation:

The student has asked to find the gradient of the line l1 which has the equation 4x-3y+5=0. To find the gradient or slope of a line given in standard form (Ax + By + C = 0), we need to rearrange the equation in the slope-intercept form (y = mx + b), where m represents the slope. Starting with the given equation, we can isolate y on one side as follows:

1. Subtract 4x from both sides: -3y = -4x - 5
2. Divide all terms by -3 to solve for y: y = (4/3)x + (5/3)

Thus, the gradient of the line is 4/3.

Answer 2

The gradient is the same as the slope. To find the slope, let's convert this from standard form to slope-intercept form.

4x - 3y + 5 = 0

4x + 5 = 3y

4/3x + 5/3 = y therefore the answer is 4/3.